Resolution No. 0309-93: Technical and Actuarial Provisions for the Establishment of the Mathematical Reserve of Insurance from the Private Pension System

Lima, June 18, 1993
Superintendence of Banking and Insurance Resolution No. 309-93

The Superintendent of Banking and Insurance:

Having seen the proposal submitted by the Adjunct Superintendence of Insurance, for the approval of the technical bases for the calculation of reserves for invalidity, survivorship, and burial expense insurance, contracted by Private Pension Fund Administrators (AFP) with insurance companies, in favor of workers affiliated with the Private System for the Administration of Pension Funds;

CONSIDERING:

That Article 38 of Law Decree No. 25897 establishes that the benefits in favor of workers incorporated into the Private System for the Administration of Pension Funds (SPP) are exclusively those of retirement, invalidity, survivorship, and burial expenses;

That the pension risks of Invalidity, Survivorship, and Burial Expenses, according to Article 48 of Law Decree No. 25897, may be covered by insurance companies established in the country and that have official authorization to operate granted by the Superintendence of Banking and Insurance;

That retirement pensions for affiliates of the AFPs may also be attended to by insurance companies that meet the aforementioned requirements, under the modality of personal or family life annuity, as provided in Article 42 of the same Law Decree;

That subsection d) of Section B of Article 7 of Resolution No. 063-93-EF/SAFP provides that, among the technical aspects that must be contained in the proposals submitted by insurance companies, they must indicate the mortality tables to be used for the calculation of technical reserves for the risks they contract with the AFPs, in favor of workers affiliated with the SPP;

That it is necessary to establish the technical interest rate for the commutation of the Mortality Tables; as well as to establish the formulas for the calculation of the technical reserves for the aforementioned pension risks;

Being in accordance with the opinion of the Technical Advisory of Insurance and the General Directorate of Legal Advisory;

In exercise of the attribution conferred by subsection w) of Article 7 of its Organic Law - Law Decree No. 25987 - and in conformity with what is provided in Article 264 of the General Law of Banking, Financial, and Insurance Institutions - Legislative Decree No. 637;

RESOLVES:

Article 1.- Authorize the use of the Chilean Mortality Table for the calculation of reserves for the insurance referred to in Articles 48 and 49 of Law Decree No. 25897, which is indicated below:

1. Invalidity

• Mortality Table MI-85-H (for men)
• Mortality Table MI-85-M (for women)

2. Survivorship (beneficiaries)

• Mortality Table B-85-H (for men)
• Mortality Table B-85-M (for women)

3. Life Annuity of the affiliated worker

• Mortality Table RV-85-H (for men)
• Mortality Table RV-85-M (for women)

Article 2.- Authorize the application of three percent (3%) as the annual technical interest rate for the commutation of the Mortality Tables, whose values are obtained with the equation and constants indicated in the following article.

Article 3.- The Mortality Tables authorized by this Circular obey the following Makeham equation:

qx = 1 - s.g c^x

(c-1) with the constants indicated below: (The constant c is raised to the power of x)

Ages (years)	Constant MI-85-H	MI-85-M
0 to 70	c: 1.072963417	1.078598208
g: 0.996723467	0.998686190
---	---
s: 0.985449773	0.990990544
70 to 110	c: 1.086562220	1.101361529
g: 0.998624505	0.999697423
---	---
s: 0.992050395	0.996745335

B-85-H	B-85-M
10 to 70	c: 1.087362757
g: 0.998759634	0.999640543
---	---
s: 0.999916758	0.999886798
70 to 110	c: 1.090857469
g: 0.999145888	0.999805878
---	---
s: 0.995970826	0.999209499

RV-85-H	RV-85-M
20 to 70	c: 1.089736350
g: 0.999214025	0.999767311
---	---
s: 0.999738701	0.999834258
70 to 110	c: 1.096209882
g: 0.999525667	0.999923115
---	---
s: 0.999140668	0.998779052

Article 4.- For the calculation of the Mathematical Reserves, which shall have the character of minimum and mandatory, for the pension insurance of Invalidity, Survivorship, and Burial Expenses referred to in Article 48 of Law Decree No. 25897 and Article 100 of Supreme Decree No. 206-92-EF, the following definitions and technical bases shall be taken:

a) Mathematical Reserve
It is the present value of the future obligations of the insurance companies upon the occurrence of accidents covered by the insurance.

b) Mortality Tables

1. For Invalidity Insurance of Affiliates
   To determine the present value of the insurance company's obligations during the transitional and deferred periods of the accidents covered by the insurance, the following tables shall be used:

• Total Invalids:
  For the transitional and deferred periods, tables MI-85-H and MI-85-M shall be used.
• Partial Invalids:
  For the transitional period, tables MI-85-H and MI-85-M shall be used, and for the deferred period, tables B-85-H and B-85-M shall be used.

2. For Life Annuities
   In the calculation of reserves for life annuity insurance, the following tables shall be used:

• Mortality Tables for Life Annuity Rentiers RV-85-H and RV-85-M.
  These tables shall be used in the calculation of reserves for non-invalid affiliates covered by old-age pension, under the modalities of immediate or deferred life annuity insurance.
• Mortality Tables for Beneficiaries B-85-H and B-85-M for the calculation of reserves for non-invalid beneficiaries.
• Mortality Tables for Invalids MI-85-H and MI-85-M for the calculation of reserves for invalid beneficiaries.

c) Formulas
The required capitals or technical reserves that insurance companies covering pension risks must establish shall be calculated according to the formulas appearing in the Annex of this Resolution, applying the percentages for each beneficiary established in Article 100 of Supreme Decree No. 206-92/EF and Annex No. 2 approved by Resolution No. 063-93-EF/SAFP.

Register, communicate, and publish.

LUIS CORTAVARRÍA CHECKLEY
Superintendent of Banking and Insurance

ANNEX
FORMULAS FOR THE CALCULATION OF RESERVES FOR PENSION INSURANCE TEMPORARY REGIME

I. NOMENCLATURE TO BE USED
x : actuarial age of the affiliate for whom the reserve is being calculated (whether man or woman) y : actuarial age of the beneficiary at the date of calculation of the reserve (whether man or woman) t : difference between 18 years and the age of the child beneficiary for whom the reserve is being calculated. f : number of years remaining to pay the additional contribution

II. FORMULAS

1. INVALIDITY

1.1 INVALID

• Transitional Period
  11
  Nx - Nx+f - ----- (Dx - Dx+f)
  V. ACTUAL = 12 24
  Dx

• Deferred Period
  11
  Nx+f - ----- Dx+f
  24
  V. ACTUAL = 12
  Dx

1.2 BENEFICIARIES WITH RIGHT TO LIFE ANNUITIES

• Transitional Period
  11 11
  Ny - Ny+f - ---- (Dy - Dy+f) Ny - Ny-f - ---- Dxy - Dx+f : y+f 24 24 A = 12 ------ - ------ Dy Dy

• Deferred Period
  11 11
  Ny+f - --- Dy+f Nx+f:y+f - ---- (Dx+f:y+f)
  24 24
  V. Actual = 12 ------ - ------
  Dy Dxy

This formula serves for the calculation of the reserve for:

• Spouse or Cohabiting Partner
• Totally or partially invalid child
• Mother of the affiliate
• Father of the affiliate

1.3 BENEFICIARIES WITH RIGHT TO TEMPORARY PENSIONS

• Transitional Period
  11 11
  Ny - Ny+f - --- (Dy - Dy+f) Nxy - Nx+f:y+f - ---- Dxy - Dx+f:y+f 24 24 A = 12 ------ - ------ Dy Dxy

• Deferred Period
  11 11
  Ny+f - N18 - --- (Dy+f - D18) Nx+f:y+f - Nx+t:18 - ---- Dx+f:y+f - Dx+t:18 24 24 A = 12 ------ - ------ Dy Dxy

These formulas serve for the calculation of the reserve for non-invalid children

1.4 BURIAL EXPENSES:
Mx
V. ACTUAL = ------ K
Dx
K = capital authorized by SAFP

2. SURVIVORSHIP

2.1 BENEFICIARIES WITH RIGHT TO LIFE ANNUITIES
Ny 11
V. ACTUAL = 12 ---- - ----
Dy 24

This formula serves for the calculation of the reserve for:

• Spouse or Cohabiting Partner
• Totally or partially invalid child
• Mother of the affiliate
• Father of the affiliate

2.2 BENEFICIARIES WITH RIGHT TO TEMPORARY PENSIONS
11
Ny - N18 - --- (Dy - D18)
24
V. ACTUAL = 12 ------
Dy

Used to determine reserve for:

• Non-invalid children

3. OLD AGE
   The formulas for old-age life annuities are the same as those indicated in section 1.
   INVALIDITY, considering the value of the nomenclature: f = 0